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The beam is sent to the plane mirror which is put on the center of this circular plane and reflected from the point $K$. When the plane mirror is rotated $10°$ in the direction of arrow, the beam is being reflected from the point $L$. Determine the lenght of the arc $KL$.

We need to have that $KL = 10°$.However, when I convert degree to radian, it seems to be $1.74778...$ which is not correct. Therefore, I didn't get how we found $\dfrac{1}{18}$.

UPDATE:

the question should be ''How much πr is the lenght of the arc KL?''. Otherwise, it won't make any sense, right? impossible to calculate the lenght without given radius. Thereby, we can try to find it in terms of $\pi r$.

Regards!

Busi
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  • whats the radius of the circle?? – The Integrator May 19 '18 at 11:42
  • @TheIntegrator That's not given. I think I misread it because we cannot solve this question without knowing the radius. Hence the question should be ''How much $\pi r$ is the lenght of the arc KL'' – Busi May 19 '18 at 11:43
  • Probably , you should recheck whether you've got the question right. – The Integrator May 19 '18 at 11:44
  • @TheIntegrator I've checked it out a sec ago. the question is ''How much $\pi r$ is the lenght of the arc KL''. Otherwise, it won't make any sense right? impossible to calculate the lenght without given radius. Hence we can try finding it in terms of $\pi r$. – Busi May 19 '18 at 11:46
  • yes it is quiet impossible, in that case $\frac1{18}$ is correct. – The Integrator May 19 '18 at 11:47
  • @TheIntegrator Could you explain how you got that answer? – Busi May 19 '18 at 11:48
  • $\pi^c = 180^\circ\implies 1^\circ = \frac{\pi^c}{180}$.

    Therefore , $10^\circ = 10\cdot\frac{\pi^c}{180} = \frac{\pi^c}{18}$. So arc length $l = r\cdot\theta = r\cdot\frac{\pi}{18}$Since it is how many $\pi\cdot r$ the length is the answer is $\frac{1}{18}$

     – The Integrator May 19 '18 at 11:51
  • @TheIntegrator So, is it correct to say that the arc KL is $10^\circ$ ? – Busi May 19 '18 at 11:58
  • No it is not . It is $10^\circ$ iff $r= 1$ unit. – The Integrator May 19 '18 at 12:01
  • @TheIntegrator Therefore, ''Determine the lenght of the arc $KL$'' is wrong, right? It should've been ''How much $πr$ is the lenght of the arc $KL$'' – Busi May 19 '18 at 12:02
  • yes it is wrong – The Integrator May 19 '18 at 12:04

1 Answers1

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The KL arc angle is $(50 + 50) - (40 + 40) = 20$ deg

So the arc length is $\frac{1}{9}\pi r$

Phil H
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